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Design, construction, and validation of a new boundary layer rake for full-scale testing
Flow Measurement and Instrumentation 26 (2012) 30–36
Contents lists available at SciVerse ScienceDirect
Flow Measurement and Instrumentation journal homepage: www.elsevier.com/locate/flowmeasinst
Design, construction, and validation of a new boundary layer rake for full-scale testing A. Elham ∗ , G.M.R. Van Raemdonck, M.J.L. van Tooren Delft University of Technology, Kluyverweg 1, 2629HS Delft, The Netherlands
article
info
Article history: Received 15 August 2011 Received in revised form 15 March 2012 Accepted 1 April 2012 Keywords: Boundary layer rake Road vehicle aerodynamics Full-scale testing
abstract A new suitable boundary layer rake design is presented to conduct measurements during full-scale testing of vehicles. The new rake is adjustable and can be installed in three different configurations. The angle between the tubes’ support and the rake pedestal can be changed to capture the velocity profile on different vehicle locations with different boundary layer thicknesses. The rake is equipped with total pressure, static pressure, and Preston tubes. With the aid of numerical simulations, the rake support dimension and tube lengths are dimensioned. The results of finite-element stress analysis on the rake structure are presented as well. A series of wind tunnel experiments has been performed to validate the new rake. In these tests, the rake was successfully validated at different installation angles and cross-wind situations. © 2012 Elsevier Ltd. All rights reserved.
1. Introduction The need for higher efficiency and lower emissions is driving automotive industries to reduce the fuel consumption of road transport vehicles. Enhancement of the aerodynamics of heavy duty vehicles is one of the most effective ways to minimize fuel consumption. Heavy-duty transport vehicles, such as trucks and trailers, can be aerodynamically characterized as bluff bodies. In recent years, various research projects have been focused on the reduction of the aerodynamic drag of transport vehicles. Attached flow shaping, trapped vortexes, undercarriage skirts, vortex strakes, and boat tail plates have been investigated for trailer drag reduction [1–3]. Quantifying the flow field around trailer–tractor combinations is one of the challenges in the field of vehicle aerodynamics. The flow over these bodies is three dimensional, turbulent, and contains regions of highly separated flow which are unsteady in time. Currently, computational simulation is not able to provide a good prediction of the flow characteristics such as a boundary layer profile. Experimental methods also need special considerations [4]. An alternative way to reduce the total drag of a bluff body is by applying guiding vanes at the rear end [5]. These vanes are in essence airfoil-shaped deflectors. An impression of this concept on a trailer can be seen in Fig. 1. The airfoils are placed in the boundary layer, inducing a lift force and thus circulation. This circulation bends the shear layer of the model inwardly, which increases the local static pressure and thus reduces the base pressure. The position of the guiding vanes within the boundary layer is crucial
∗
Corresponding author. Tel.: +31 15 2781601; fax: +31 15 2789564. E-mail address: [email protected] (A. Elham).
0955-5986/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.flowmeasinst.2012.04.001
with respect to the maximized drag reduction. In order to optimize the position of these vanes, the boundary layer profile should be measured. In 2005, the faculty of Aerospace Engineering of Delft University of Technology initiated a research program to improve the aerodynamic drag level of heavy-duty vehicles [5]. A series of wind tunnel and road tests is planned to study the boundary layer characteristics of trailers and trucks. The present research covers the design and construction of a measuring device to study the boundary layer velocity profile and to measure the skin friction coefficient on a full-scale trailer during road testing. Measurement of the skin friction coefficient is helpful for verification of the measured boundary layer velocity profile. There are several methods to measure the wall skin friction [6]. One is to use Clauser charts. As soon as the velocity profile is measured, it is possible to calculate the local skin friction coefficient by means of these charts. Allen and Tudor [7] presented a series of such charts for a wide range of Mach numbers. Another method for skin friction measurements is the use of a Preston tube. A Preston tube is a Pitot tube that rests on the wall (see Fig. 2). Applying the logarithmic law of the wall, the local skin friction can be determined from the pressure measured by the Preston tube [8]. Calibration methods presented by Patel [9] or Bechert [10] can be used to obtain the skin friction coefficient on a flat plat by using Preston tubes. 2. Design considerations Conducting measurements on the development of a turbulent boundary layer velocity profile of a full-scale, standard, hard covered trailer that is 13.6 m long requires special considerations.
A. Elham et al. / Flow Measurement and Instrumentation 26 (2012) 30–36
31
Fig. 1. Guiding vanes installed at the rear end of a trailer. Fig. 3. Perspective view of the boundary layer rake installed vertically.
Fig. 2. A Preston tube.
With the aid of Eq. (1), taken from [11], which is derived based on flat-plate turbulent boundary layer theory, one can calculate, for an air speed of 85 km/h, the boundary layer thicknesses of a flat plate at x = 1 m and x = 13 m to be about 2 cm and 17 cm, respectively. In this equation δ is the boundary layer thickness, x is the longitudinal coordinate and Rex is the local Reynolds number.
δ = 0.383
x Re0x .2
.
(1)
The analytical solution results in a wide range of boundary layer thicknesses on the side and top surfaces of the trailer. If the effect of the presence of the tractor is included, the boundary layer will be even thicker. The measurement of such a wide range of boundary layer thicknesses, with an acceptable accuracy, necessitates a new measuring device which can be adjusted for different streamwise positions. Another important consideration is the effect of cross wind. The boundary layer rake should be designed to be used in a series of road tests. In such a situation, cross winds are unavoidable. In order to minimize measurement errors, a ±10° angle between the wind velocity vector and the probe’s longitudinal axis is considered as another design requirement [5]. In order to have a complete development of the boundary layer profile, the velocity profile of the boundary layer should be measured in different streamwise positions between the front and the rear edges of the trailer. The rake should be able to be removed from one position and installed in the next with a minimum amount of time and effort. Easy installation without drilling or cutting the surface of the trailer is required. 3. New rake design Considering all the requirements, an adjustable rake that can be installed in three different angles θ was designed. The designed rake consists of a horizontal pedestal, a probe support, and two auxiliary supports, as illustrated in Fig. 4. The auxiliary supports are used to install the rake at θ = 60° and θ = 30° angles. Figs. 3 and 4 illustrate the designed rake configuration.
At the lowest installation angle, Fig. 4(c), the rake can measure the boundary layer velocity profile near the front edge of trailer where the boundary layer is relatively thin. In this configuration, it is possible to have more clustered probes near the surface. Going downstream, the boundary layer thickness increases, and the rake can be installed at a higher angle; see Fig. 4(b). Finally, near the rear edge of the trailer, the thickest boundary layer can be measured by installing the rake at a 90° angle; see Fig. 4(a). A total of 31 probes can be installed on the support. Three of the tubes are static pressure probes; the rest are total pressure probes (see Fig. 5). There are also three Preston tubes installed in three installation positions of the rake on the pedestal. As mentioned before, due to the test-specific conditions, the rake should be able to measure true pressures in the presence of cross wind. According to the work of Goldstein [6], errors in the total pressure value constitute less than 5% of the free stream flow dynamic pressure, while the angles of misalignment are less than 5°. Also, Gracey [12] showed that the insensitivity angle of a total pressure tube can be increased by changing the nose shape of the tube to a conical entry. Gracey’s experiments [12] indicated a 27° angle of insensitivity for a tube by 30° conical entry. So, in order to increase the accuracy of the total pressure measurements, a tube with a 30° conical entry is chosen for the total pressure probes (see Fig. 6). Errors in the static pressure measurements depend on the shape and location of the pressure orifices in the tubes. The orifices should be located far enough from the nose of the probe to be unaffected by the pressure gradient it causes. This distance should be at least three or four times the tube diameter [12]. To increase the insensitivity angle of the static pressure probes, the pressure distribution around a cylinder should be considered. Fig. 7, taken from [13], shows the pressure distribution around a circular cylinder. Based on the solution of potential flow around a cylinder (Cp = 1 − 4 sin2 φ ), the pressure decreases between the stagnation point (at φ = 0°) and the maximum thickness (at φ = 90°) from Cp = 1 to Cp = −3. However, if the effect of the boundary layer is considered, the pressure at the rear side of the cylinder is much lower than that predicted for inviscid flow due to the flow separation. The location of the separation point is a function of the Reynolds number. From Fig. 7, one can observe that, for Reynolds numbers less than 105 , the minimum static pressure error around a probe occurs at radial stations of about 35° where CP = 0. Locating the orifices at ±35° from the horizontal axis can be a way to increase the insensitivity angle. Due to the three different installation angles, the angles between the orifices and the horizontal axis in each configuration are different. To overcome this problem, three different static tubes are used for each of the three different configurations. These tubes are similar, but they are installed at different radial angles
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A. Elham et al. / Flow Measurement and Instrumentation 26 (2012) 30–36
(a) 90° installation angle.
(b) 60° installation angle.
(c) 30° installation angle. Fig. 4. Designed boundary layer rake at three different installation angles.
Fig. 7. Pressure distribution around the circumference of circular cylinders [13].
Fig. 5. The total pressure tubes (shorter ones) and the static pressure tubes (longer ones) installed on the rake.
Fig. 6. Total pressure tube with conical entry.
(Fig. 8). The first tube from the bottom is appropriated for the 30° installation angle (the angle between the orifices of this tube and the horizontal axis is ±35°, when the rake is installed at θ = 30°), the second tube is for the 60° installation angle, and the last one is for the vertical condition. In the subsonic regime, the shape of the probes’ support has an effect on the upstream flow. A numerical analysis with the aid of computational fluid dynamics (CFD) is executed to find a combination of the shape of the support and the probe length, to check the influence of the support on the pressure coefficient at the entrance of the probes. Two different profiles are tested. The first profile is a wellrecognized NACA 0012 airfoil. The second one is a more
Fig. 8. Three static tubes installed with different angles.
simple profile with the same maximum thickness to chord ratio (12%); see Fig. 9. The analysis is performed with the aid of the commercially available software Fluent. Reynolds-averaged
A. Elham et al. / Flow Measurement and Instrumentation 26 (2012) 30–36 Table 1 Pressure coefficient at
x c
33
= −1.66.
Profile
Cp in the entrance of tube at 0° angle of attack
Cp in the entrance of tube at 10° angle of attack
a b
0.009 0.012
−0.0007 −0.007
(a) 0° angle of attack.
(b) 10° angle of attack. Fig. 9. Pressure distribution in front of two profiles. Table 2 Rake minimum margin of safety at different angles of installation.
Fig. 10. Dimensions of the total pressure tubes and the rake support.
Navier–Stokes (RANS) equations together with the turbulence equation obtained using Spalart–Allmaras turbulence model, are solved on two unstructured grids with about 5000 nodes for profile a and 7000 nodes for profile b. The inlet velocity was fixed to 22 m/s (Re = 9 × 104 based on the profile chord). The modified turbulence viscosity is 0.001 m/s2 . A simple solver was utilized and the operating pressure was set to zero. Calculations were done for 0° and 10° angles of attack. As illustrated in Fig. 9, for x/c < −1, profile b induces slightly more disturbance to the flow than profile a; however, the induced pressure coefficients are of the same order of magnitude. Due to its simpler shape for manufacturing, one can conclude that profile b is the better choice. The CFD results show, for x/c = −1.66 (in front of the profiles), that the pressure coefficient is around 0.01, for both 0° and 10° angles of attack, summarized in Table 1. This amount of pressure coefficient causes an uncertainty of about 1% in the pressure measurement. As mentioned above, the main aim of using the new rake is measuring the thickness of the boundary layer on the trailer to make decisions about the position of the guiding vane. The uncertainty of the boundary layer thickness measurement causes by this 1% uncertainty in the pressure measurement is of the order of few millimetres (for a 20 cm thick boundary layer), which is acceptable. Based on these results, the entrances of the probes are located at x = −1.66c: the tube length is selected to be equal to 1.66 times the support length (see Fig. 10).
Installation angle (°)
Minimum margin of safety
90 60 30
9 16 16
constructed with steel alloy AISI 340. The tubes were made of capillary tubes of the same alloy, with an inner diameter of 1.3 mm and wall thickness of 0.2 mm. A finite-element structural analysis was executed using COSMOS/Works software. In order to determine the maximum load on the rake the following assumptions were made: the wind speed is equal to 25 m/s and the wind direction is perpendicular to the rake support (90° side angle). These conditions provide the maximum load on the rake. Even though these extreme conditions are unlikely to actually happen in reality, they are considered here to test the rake’s minimum margin of safety. The loads on the rake are determined using the drag coefficient of a flat plate perpendicular to the stream. The normal force coefficient on a three-dimensional flat plate is shown in Fig. 11 at different angles in the flow. For α > 45°, the normal force coefficient is constant and equal to 1.17. For α = 30°, this coefficient is about 1.4. The reserve factor of a structure is defined as the ratio between the yield stress and the maximum von Mises stress in the structure. If the reverse factor is decreased by one, the structure’s margin of safety can be calculated. The minimum margins of safety for the rake installed at various angles are listed in Table 2. Based on these values, no structural failure is expected during the road tests. 5. Validation test
4. Structural analysis and manufacturing The rake was manufactured at Delft University of Technology. The support was manufactured by means of a CNC milling machine with an accuracy of 0.01 mm. Aluminum alloy 6082 was selected for the pedestal and probe support. The auxiliary support was
A series of tests was executed in the Open Jet Facility (OJF) of the faculty of Aerospace Engineering of Delft University of Technology to validate the new rake. The OJF has an octagonal 285×285 cm test section. The maximum velocity in the test section is about 35 m/s. A schematic view of the OJF is shown in Fig. 12.
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A. Elham et al. / Flow Measurement and Instrumentation 26 (2012) 30–36
2 Circular plate Square plate
1.8 1.6
Cnormal
1.4 1.2 1 0.8 0.6 0.4 0.2 0
0
10
20
30
40
50
60
70
80
90
Fig. 13. Boundary layer rake installed on the wind tunnel nozzle.
α [deg] Fig. 11. Normal force coefficient of plates having square and circular shape. Source: Reproduced from [13].
Fig. 12. Schematic view of the OJF. Fig. 14. Disturbing element installed in the wind tunnel nozzle.
400
300
y [mm]
All pressure measurements during the test had an uncertainty of 0.01% of the full-scale pressure. The uncertainty of the temperature measurement was ±0.02°C. In the first test, the rake was installed on the edge of the nozzle, as shown in Fig. 13. A thicker boundary layer is induced by placing a disturbing element (DE) in front of the rake inside the nozzle (Figs. 13–14). The dimensions of the DE are 99 × 99 cm, and the average thickness is 4 cm. The flow velocity during all tests was constant and equal to 10 ± 0.2 m/s. The boundary layer profile was measured by the rake under six different conditions. The first three measurements were taken parallel to the flow direction, for each installation angle. Then, the rake was placed at a 10° angle to the flow direction (β ), and tested again at the three installation angles. The velocity profile inside the boundary layer was measured by an external Pitot-static tube. The velocity profiles captured by the rake are given in Fig. 15, for all six different test conditions. In this figure, the velocity (V ) is normalized by the flow velocity at the edge of boundary layer (Ve ). However, the vertical distance from the wall (y) is plotted in millimeters to give an impression of the absolute thickness of the boundary layer. Vortexes generated by the DE are the cause of the differences in velocity profile. Even though this DE does not cover the entire width of the nozzle (Fig. 14), two vortexes are generated from the edges of the DE. The contours of the velocity components simulated by a qualitative CFD analysis of the nozzle with the DE (Fig. 16) illustrate the presence of those vortexes. In order to compare the results of the rake and the Pitot tube, the velocity profile was measured with the Pitot tube in two conditions: a vertical line aligned with the rake probes at a 90° installation angle and a 30° slanted line aligned with the rake
200
100
0 0.7
0.8
0.9 V/Ve
1
Fig. 15. Boundary layer velocity profile measured by the rake installed in the wind tunnel nozzle.
probes at a 30° installation angle. The velocity profiles measured by the rake and the Pitot tube are shown in Fig. 17. In the second test, the boundary layer velocity profile was measured on a 3 m long flat plate installed in the wind tunnel test section right behind the nozzle. The rake was placed 2.5 m behind the leading edge of the plate. The boundary layer velocity profile
A. Elham et al. / Flow Measurement and Instrumentation 26 (2012) 30–36
(a) z-component.
35
(b) x-component.
y [mm]
y [mm]
Fig. 16. Contours of flow velocity after the disturbing element (DE) in the wind tunnel nozzle.
200
200
100 100
0 0.7
0 0.7 0.8
0.9 V/Ve
1
Fig. 17. Boundary layer velocity profile measured by the rake and by the Pitot-static tube.
0.8
0.9 V/Ve
1
Fig. 18. Boundary layer velocity profile measured by the rake installed on the flat plate.
Table 3 Skin friction coefficient. Measurement method
Skin friction coefficient
Preston tube—Bechert calibration [10] Preston tube—Patel calibration [9] Charts from [7]
0.00327 0.00325 0.0033
was measured in the same six conditions as used in test 1. The flow velocity was taken equal to 10 ± 0.2 m/s, and it remained constant for all six test cases. Fig. 18 shows the velocity profiles for the rake aligned with the flow direction, as well as the velocity profile at a 10° angle between the rake and the flow direction. The wall skin friction coefficient was measured by means of the Preston tubes installed on the rake pedestal, and it was compared with the coefficient calculated using the charts presented in [7]. In this method, the normalized velocities (V /Ve ) are plotted versus µ µ the parameter µ e Ry , where µ e is the ratio of flow viscosity at the w w edge of the boundary layer to the flow viscosity at the wall and Ry is the Reynolds number based on y (see Fig. 19). The results of each are shown in Table 3. In the final step, the results of the tests were compared with turbulent boundary layer theory. Fig. 20 shows the turbulent boundary layer velocity profile measured with the rake, in different
Fig. 19. Measurement of the skin friction coefficient using the charts in [7].
installation conditions, in dimensionless units, in comparison with the results of the logarithmic law of the wall [11], which is defined as U+ =
1 k
ln(y+ ) + C ,
(2)
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A. Elham et al. / Flow Measurement and Instrumentation 26 (2012) 30–36
26
test. The unique design feature of this rake is the adjustability of the installation. The rake can be installed at three different angles perpendicular to the surface, to measure the boundary layer profiles, in different locations on the top and side of a trailer. The results of the wind tunnel tests show that the rake satisfies the design requirements. The velocity profile measured by the rake has been matched with the velocity profile measured by a Pitotstatic tube at different installation angles. The results show a good agreement between the experiments and the theory (logarithmic law of the wall).
24
U + 22
20
References
18 100
1x103
y
1x104
+
Fig. 20. Turbulent boundary layer velocity profile.
where U + is the dimensionless velocity, which is defined as the mean velocity U divided by the friction velocity uτ . The friction
velocity is defined as uτ =
τw , ρ
where τw is the wall shear stress, ρu y
which is measured with the Preston tubes. y+ = µτ , while k and C are constants. Schlichting [11] suggested the values k = 0.41 and C = 5.5. The logarithmic law of the wall is valid only in the inner layer of the boundary layer, which is also called the ‘‘wall layer’’. Fig. 20 shows good agreement between the results of the experiment and the applied theory in the inner layer. 6. Conclusion A new boundary layer rake has been designed to measure the boundary layer velocity profile on a trailer during a road
[1] Wood RM. Impact of advanced aerodynamic technology on transportation energy consumption. SAE technical paper no. 2004-01-1306. 2004. [2] Wood RM, Bauer SXS. Simple and low-cost aerodynamic drag reduction devices for tractor-trailer trucks. SAE technical paper no. 2003-01-3377. 2003. [3] Saltzman EJ, Meyer RR Jr. A reassessment of heavy-duty truck aerodynamic design features and priorities. NASA technical paper no. 1999-206574. June 1999. [4] A multi-year program plan for the aerodynamic design of heavy vehicle. Joint Written by Lawrence Livermore National Laboratory. Sandia National Laboratories. University of Southern California. California Institute of Technology and NASA Ames Research Center [5] Van Raemdonck GMR. Design of low drag bluff road vehicles. Doctoral design. Delft University of Technology. Faculty of Aerospace Engineering. May, 2012. [6] Goldstein RJ. Fluid mechanics measurements. Hemisphere Publishing Corporation; 1993. [7] Allen JM, Tudor DH. Charts for interpolation of local skin friction from experimental turbulent velocity profile. NASA SP-3048. 1969. [8] Preston JH. The determination of turbulent skin friction by means of Pitot tube. J Roy Aero Soc 1954;58. [9] Patel VC. Calibration of the Preston tube and limitation on its use in pressure gradient. J Fluid Mech 1965;23:185–208. [10] Bechert DW. Calibration of Preston tube. J AIAA 1995;34(1):205–6. [11] Schlichting H. Boundary layer theory. New York: McGraw-Hill; 1979. [12] Gracey W. Measurement of aircraft speed and altitude. NASA Reference Publication 1046; 1980. [13] Hoerner SF. Fluid-dynamic drag; practical information on aerodynamic drag and hydrodynamic resistance. Midland Park; 1965.
Contents lists available at SciVerse ScienceDirect
Flow Measurement and Instrumentation journal homepage: www.elsevier.com/locate/flowmeasinst
Design, construction, and validation of a new boundary layer rake for full-scale testing A. Elham ∗ , G.M.R. Van Raemdonck, M.J.L. van Tooren Delft University of Technology, Kluyverweg 1, 2629HS Delft, The Netherlands
article
info
Article history: Received 15 August 2011 Received in revised form 15 March 2012 Accepted 1 April 2012 Keywords: Boundary layer rake Road vehicle aerodynamics Full-scale testing
abstract A new suitable boundary layer rake design is presented to conduct measurements during full-scale testing of vehicles. The new rake is adjustable and can be installed in three different configurations. The angle between the tubes’ support and the rake pedestal can be changed to capture the velocity profile on different vehicle locations with different boundary layer thicknesses. The rake is equipped with total pressure, static pressure, and Preston tubes. With the aid of numerical simulations, the rake support dimension and tube lengths are dimensioned. The results of finite-element stress analysis on the rake structure are presented as well. A series of wind tunnel experiments has been performed to validate the new rake. In these tests, the rake was successfully validated at different installation angles and cross-wind situations. © 2012 Elsevier Ltd. All rights reserved.
1. Introduction The need for higher efficiency and lower emissions is driving automotive industries to reduce the fuel consumption of road transport vehicles. Enhancement of the aerodynamics of heavy duty vehicles is one of the most effective ways to minimize fuel consumption. Heavy-duty transport vehicles, such as trucks and trailers, can be aerodynamically characterized as bluff bodies. In recent years, various research projects have been focused on the reduction of the aerodynamic drag of transport vehicles. Attached flow shaping, trapped vortexes, undercarriage skirts, vortex strakes, and boat tail plates have been investigated for trailer drag reduction [1–3]. Quantifying the flow field around trailer–tractor combinations is one of the challenges in the field of vehicle aerodynamics. The flow over these bodies is three dimensional, turbulent, and contains regions of highly separated flow which are unsteady in time. Currently, computational simulation is not able to provide a good prediction of the flow characteristics such as a boundary layer profile. Experimental methods also need special considerations [4]. An alternative way to reduce the total drag of a bluff body is by applying guiding vanes at the rear end [5]. These vanes are in essence airfoil-shaped deflectors. An impression of this concept on a trailer can be seen in Fig. 1. The airfoils are placed in the boundary layer, inducing a lift force and thus circulation. This circulation bends the shear layer of the model inwardly, which increases the local static pressure and thus reduces the base pressure. The position of the guiding vanes within the boundary layer is crucial
∗
Corresponding author. Tel.: +31 15 2781601; fax: +31 15 2789564. E-mail address: [email protected] (A. Elham).
0955-5986/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.flowmeasinst.2012.04.001
with respect to the maximized drag reduction. In order to optimize the position of these vanes, the boundary layer profile should be measured. In 2005, the faculty of Aerospace Engineering of Delft University of Technology initiated a research program to improve the aerodynamic drag level of heavy-duty vehicles [5]. A series of wind tunnel and road tests is planned to study the boundary layer characteristics of trailers and trucks. The present research covers the design and construction of a measuring device to study the boundary layer velocity profile and to measure the skin friction coefficient on a full-scale trailer during road testing. Measurement of the skin friction coefficient is helpful for verification of the measured boundary layer velocity profile. There are several methods to measure the wall skin friction [6]. One is to use Clauser charts. As soon as the velocity profile is measured, it is possible to calculate the local skin friction coefficient by means of these charts. Allen and Tudor [7] presented a series of such charts for a wide range of Mach numbers. Another method for skin friction measurements is the use of a Preston tube. A Preston tube is a Pitot tube that rests on the wall (see Fig. 2). Applying the logarithmic law of the wall, the local skin friction can be determined from the pressure measured by the Preston tube [8]. Calibration methods presented by Patel [9] or Bechert [10] can be used to obtain the skin friction coefficient on a flat plat by using Preston tubes. 2. Design considerations Conducting measurements on the development of a turbulent boundary layer velocity profile of a full-scale, standard, hard covered trailer that is 13.6 m long requires special considerations.
A. Elham et al. / Flow Measurement and Instrumentation 26 (2012) 30–36
31
Fig. 1. Guiding vanes installed at the rear end of a trailer. Fig. 3. Perspective view of the boundary layer rake installed vertically.
Fig. 2. A Preston tube.
With the aid of Eq. (1), taken from [11], which is derived based on flat-plate turbulent boundary layer theory, one can calculate, for an air speed of 85 km/h, the boundary layer thicknesses of a flat plate at x = 1 m and x = 13 m to be about 2 cm and 17 cm, respectively. In this equation δ is the boundary layer thickness, x is the longitudinal coordinate and Rex is the local Reynolds number.
δ = 0.383
x Re0x .2
.
(1)
The analytical solution results in a wide range of boundary layer thicknesses on the side and top surfaces of the trailer. If the effect of the presence of the tractor is included, the boundary layer will be even thicker. The measurement of such a wide range of boundary layer thicknesses, with an acceptable accuracy, necessitates a new measuring device which can be adjusted for different streamwise positions. Another important consideration is the effect of cross wind. The boundary layer rake should be designed to be used in a series of road tests. In such a situation, cross winds are unavoidable. In order to minimize measurement errors, a ±10° angle between the wind velocity vector and the probe’s longitudinal axis is considered as another design requirement [5]. In order to have a complete development of the boundary layer profile, the velocity profile of the boundary layer should be measured in different streamwise positions between the front and the rear edges of the trailer. The rake should be able to be removed from one position and installed in the next with a minimum amount of time and effort. Easy installation without drilling or cutting the surface of the trailer is required. 3. New rake design Considering all the requirements, an adjustable rake that can be installed in three different angles θ was designed. The designed rake consists of a horizontal pedestal, a probe support, and two auxiliary supports, as illustrated in Fig. 4. The auxiliary supports are used to install the rake at θ = 60° and θ = 30° angles. Figs. 3 and 4 illustrate the designed rake configuration.
At the lowest installation angle, Fig. 4(c), the rake can measure the boundary layer velocity profile near the front edge of trailer where the boundary layer is relatively thin. In this configuration, it is possible to have more clustered probes near the surface. Going downstream, the boundary layer thickness increases, and the rake can be installed at a higher angle; see Fig. 4(b). Finally, near the rear edge of the trailer, the thickest boundary layer can be measured by installing the rake at a 90° angle; see Fig. 4(a). A total of 31 probes can be installed on the support. Three of the tubes are static pressure probes; the rest are total pressure probes (see Fig. 5). There are also three Preston tubes installed in three installation positions of the rake on the pedestal. As mentioned before, due to the test-specific conditions, the rake should be able to measure true pressures in the presence of cross wind. According to the work of Goldstein [6], errors in the total pressure value constitute less than 5% of the free stream flow dynamic pressure, while the angles of misalignment are less than 5°. Also, Gracey [12] showed that the insensitivity angle of a total pressure tube can be increased by changing the nose shape of the tube to a conical entry. Gracey’s experiments [12] indicated a 27° angle of insensitivity for a tube by 30° conical entry. So, in order to increase the accuracy of the total pressure measurements, a tube with a 30° conical entry is chosen for the total pressure probes (see Fig. 6). Errors in the static pressure measurements depend on the shape and location of the pressure orifices in the tubes. The orifices should be located far enough from the nose of the probe to be unaffected by the pressure gradient it causes. This distance should be at least three or four times the tube diameter [12]. To increase the insensitivity angle of the static pressure probes, the pressure distribution around a cylinder should be considered. Fig. 7, taken from [13], shows the pressure distribution around a circular cylinder. Based on the solution of potential flow around a cylinder (Cp = 1 − 4 sin2 φ ), the pressure decreases between the stagnation point (at φ = 0°) and the maximum thickness (at φ = 90°) from Cp = 1 to Cp = −3. However, if the effect of the boundary layer is considered, the pressure at the rear side of the cylinder is much lower than that predicted for inviscid flow due to the flow separation. The location of the separation point is a function of the Reynolds number. From Fig. 7, one can observe that, for Reynolds numbers less than 105 , the minimum static pressure error around a probe occurs at radial stations of about 35° where CP = 0. Locating the orifices at ±35° from the horizontal axis can be a way to increase the insensitivity angle. Due to the three different installation angles, the angles between the orifices and the horizontal axis in each configuration are different. To overcome this problem, three different static tubes are used for each of the three different configurations. These tubes are similar, but they are installed at different radial angles
32
A. Elham et al. / Flow Measurement and Instrumentation 26 (2012) 30–36
(a) 90° installation angle.
(b) 60° installation angle.
(c) 30° installation angle. Fig. 4. Designed boundary layer rake at three different installation angles.
Fig. 7. Pressure distribution around the circumference of circular cylinders [13].
Fig. 5. The total pressure tubes (shorter ones) and the static pressure tubes (longer ones) installed on the rake.
Fig. 6. Total pressure tube with conical entry.
(Fig. 8). The first tube from the bottom is appropriated for the 30° installation angle (the angle between the orifices of this tube and the horizontal axis is ±35°, when the rake is installed at θ = 30°), the second tube is for the 60° installation angle, and the last one is for the vertical condition. In the subsonic regime, the shape of the probes’ support has an effect on the upstream flow. A numerical analysis with the aid of computational fluid dynamics (CFD) is executed to find a combination of the shape of the support and the probe length, to check the influence of the support on the pressure coefficient at the entrance of the probes. Two different profiles are tested. The first profile is a wellrecognized NACA 0012 airfoil. The second one is a more
Fig. 8. Three static tubes installed with different angles.
simple profile with the same maximum thickness to chord ratio (12%); see Fig. 9. The analysis is performed with the aid of the commercially available software Fluent. Reynolds-averaged
A. Elham et al. / Flow Measurement and Instrumentation 26 (2012) 30–36 Table 1 Pressure coefficient at
x c
33
= −1.66.
Profile
Cp in the entrance of tube at 0° angle of attack
Cp in the entrance of tube at 10° angle of attack
a b
0.009 0.012
−0.0007 −0.007
(a) 0° angle of attack.
(b) 10° angle of attack. Fig. 9. Pressure distribution in front of two profiles. Table 2 Rake minimum margin of safety at different angles of installation.
Fig. 10. Dimensions of the total pressure tubes and the rake support.
Navier–Stokes (RANS) equations together with the turbulence equation obtained using Spalart–Allmaras turbulence model, are solved on two unstructured grids with about 5000 nodes for profile a and 7000 nodes for profile b. The inlet velocity was fixed to 22 m/s (Re = 9 × 104 based on the profile chord). The modified turbulence viscosity is 0.001 m/s2 . A simple solver was utilized and the operating pressure was set to zero. Calculations were done for 0° and 10° angles of attack. As illustrated in Fig. 9, for x/c < −1, profile b induces slightly more disturbance to the flow than profile a; however, the induced pressure coefficients are of the same order of magnitude. Due to its simpler shape for manufacturing, one can conclude that profile b is the better choice. The CFD results show, for x/c = −1.66 (in front of the profiles), that the pressure coefficient is around 0.01, for both 0° and 10° angles of attack, summarized in Table 1. This amount of pressure coefficient causes an uncertainty of about 1% in the pressure measurement. As mentioned above, the main aim of using the new rake is measuring the thickness of the boundary layer on the trailer to make decisions about the position of the guiding vane. The uncertainty of the boundary layer thickness measurement causes by this 1% uncertainty in the pressure measurement is of the order of few millimetres (for a 20 cm thick boundary layer), which is acceptable. Based on these results, the entrances of the probes are located at x = −1.66c: the tube length is selected to be equal to 1.66 times the support length (see Fig. 10).
Installation angle (°)
Minimum margin of safety
90 60 30
9 16 16
constructed with steel alloy AISI 340. The tubes were made of capillary tubes of the same alloy, with an inner diameter of 1.3 mm and wall thickness of 0.2 mm. A finite-element structural analysis was executed using COSMOS/Works software. In order to determine the maximum load on the rake the following assumptions were made: the wind speed is equal to 25 m/s and the wind direction is perpendicular to the rake support (90° side angle). These conditions provide the maximum load on the rake. Even though these extreme conditions are unlikely to actually happen in reality, they are considered here to test the rake’s minimum margin of safety. The loads on the rake are determined using the drag coefficient of a flat plate perpendicular to the stream. The normal force coefficient on a three-dimensional flat plate is shown in Fig. 11 at different angles in the flow. For α > 45°, the normal force coefficient is constant and equal to 1.17. For α = 30°, this coefficient is about 1.4. The reserve factor of a structure is defined as the ratio between the yield stress and the maximum von Mises stress in the structure. If the reverse factor is decreased by one, the structure’s margin of safety can be calculated. The minimum margins of safety for the rake installed at various angles are listed in Table 2. Based on these values, no structural failure is expected during the road tests. 5. Validation test
4. Structural analysis and manufacturing The rake was manufactured at Delft University of Technology. The support was manufactured by means of a CNC milling machine with an accuracy of 0.01 mm. Aluminum alloy 6082 was selected for the pedestal and probe support. The auxiliary support was
A series of tests was executed in the Open Jet Facility (OJF) of the faculty of Aerospace Engineering of Delft University of Technology to validate the new rake. The OJF has an octagonal 285×285 cm test section. The maximum velocity in the test section is about 35 m/s. A schematic view of the OJF is shown in Fig. 12.
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A. Elham et al. / Flow Measurement and Instrumentation 26 (2012) 30–36
2 Circular plate Square plate
1.8 1.6
Cnormal
1.4 1.2 1 0.8 0.6 0.4 0.2 0
0
10
20
30
40
50
60
70
80
90
Fig. 13. Boundary layer rake installed on the wind tunnel nozzle.
α [deg] Fig. 11. Normal force coefficient of plates having square and circular shape. Source: Reproduced from [13].
Fig. 12. Schematic view of the OJF. Fig. 14. Disturbing element installed in the wind tunnel nozzle.
400
300
y [mm]
All pressure measurements during the test had an uncertainty of 0.01% of the full-scale pressure. The uncertainty of the temperature measurement was ±0.02°C. In the first test, the rake was installed on the edge of the nozzle, as shown in Fig. 13. A thicker boundary layer is induced by placing a disturbing element (DE) in front of the rake inside the nozzle (Figs. 13–14). The dimensions of the DE are 99 × 99 cm, and the average thickness is 4 cm. The flow velocity during all tests was constant and equal to 10 ± 0.2 m/s. The boundary layer profile was measured by the rake under six different conditions. The first three measurements were taken parallel to the flow direction, for each installation angle. Then, the rake was placed at a 10° angle to the flow direction (β ), and tested again at the three installation angles. The velocity profile inside the boundary layer was measured by an external Pitot-static tube. The velocity profiles captured by the rake are given in Fig. 15, for all six different test conditions. In this figure, the velocity (V ) is normalized by the flow velocity at the edge of boundary layer (Ve ). However, the vertical distance from the wall (y) is plotted in millimeters to give an impression of the absolute thickness of the boundary layer. Vortexes generated by the DE are the cause of the differences in velocity profile. Even though this DE does not cover the entire width of the nozzle (Fig. 14), two vortexes are generated from the edges of the DE. The contours of the velocity components simulated by a qualitative CFD analysis of the nozzle with the DE (Fig. 16) illustrate the presence of those vortexes. In order to compare the results of the rake and the Pitot tube, the velocity profile was measured with the Pitot tube in two conditions: a vertical line aligned with the rake probes at a 90° installation angle and a 30° slanted line aligned with the rake
200
100
0 0.7
0.8
0.9 V/Ve
1
Fig. 15. Boundary layer velocity profile measured by the rake installed in the wind tunnel nozzle.
probes at a 30° installation angle. The velocity profiles measured by the rake and the Pitot tube are shown in Fig. 17. In the second test, the boundary layer velocity profile was measured on a 3 m long flat plate installed in the wind tunnel test section right behind the nozzle. The rake was placed 2.5 m behind the leading edge of the plate. The boundary layer velocity profile
A. Elham et al. / Flow Measurement and Instrumentation 26 (2012) 30–36
(a) z-component.
35
(b) x-component.
y [mm]
y [mm]
Fig. 16. Contours of flow velocity after the disturbing element (DE) in the wind tunnel nozzle.
200
200
100 100
0 0.7
0 0.7 0.8
0.9 V/Ve
1
Fig. 17. Boundary layer velocity profile measured by the rake and by the Pitot-static tube.
0.8
0.9 V/Ve
1
Fig. 18. Boundary layer velocity profile measured by the rake installed on the flat plate.
Table 3 Skin friction coefficient. Measurement method
Skin friction coefficient
Preston tube—Bechert calibration [10] Preston tube—Patel calibration [9] Charts from [7]
0.00327 0.00325 0.0033
was measured in the same six conditions as used in test 1. The flow velocity was taken equal to 10 ± 0.2 m/s, and it remained constant for all six test cases. Fig. 18 shows the velocity profiles for the rake aligned with the flow direction, as well as the velocity profile at a 10° angle between the rake and the flow direction. The wall skin friction coefficient was measured by means of the Preston tubes installed on the rake pedestal, and it was compared with the coefficient calculated using the charts presented in [7]. In this method, the normalized velocities (V /Ve ) are plotted versus µ µ the parameter µ e Ry , where µ e is the ratio of flow viscosity at the w w edge of the boundary layer to the flow viscosity at the wall and Ry is the Reynolds number based on y (see Fig. 19). The results of each are shown in Table 3. In the final step, the results of the tests were compared with turbulent boundary layer theory. Fig. 20 shows the turbulent boundary layer velocity profile measured with the rake, in different
Fig. 19. Measurement of the skin friction coefficient using the charts in [7].
installation conditions, in dimensionless units, in comparison with the results of the logarithmic law of the wall [11], which is defined as U+ =
1 k
ln(y+ ) + C ,
(2)
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A. Elham et al. / Flow Measurement and Instrumentation 26 (2012) 30–36
26
test. The unique design feature of this rake is the adjustability of the installation. The rake can be installed at three different angles perpendicular to the surface, to measure the boundary layer profiles, in different locations on the top and side of a trailer. The results of the wind tunnel tests show that the rake satisfies the design requirements. The velocity profile measured by the rake has been matched with the velocity profile measured by a Pitotstatic tube at different installation angles. The results show a good agreement between the experiments and the theory (logarithmic law of the wall).
24
U + 22
20
References
18 100
1x103
y
1x104
+
Fig. 20. Turbulent boundary layer velocity profile.
where U + is the dimensionless velocity, which is defined as the mean velocity U divided by the friction velocity uτ . The friction
velocity is defined as uτ =
τw , ρ
where τw is the wall shear stress, ρu y
which is measured with the Preston tubes. y+ = µτ , while k and C are constants. Schlichting [11] suggested the values k = 0.41 and C = 5.5. The logarithmic law of the wall is valid only in the inner layer of the boundary layer, which is also called the ‘‘wall layer’’. Fig. 20 shows good agreement between the results of the experiment and the applied theory in the inner layer. 6. Conclusion A new boundary layer rake has been designed to measure the boundary layer velocity profile on a trailer during a road
[1] Wood RM. Impact of advanced aerodynamic technology on transportation energy consumption. SAE technical paper no. 2004-01-1306. 2004. [2] Wood RM, Bauer SXS. Simple and low-cost aerodynamic drag reduction devices for tractor-trailer trucks. SAE technical paper no. 2003-01-3377. 2003. [3] Saltzman EJ, Meyer RR Jr. A reassessment of heavy-duty truck aerodynamic design features and priorities. NASA technical paper no. 1999-206574. June 1999. [4] A multi-year program plan for the aerodynamic design of heavy vehicle. Joint Written by Lawrence Livermore National Laboratory. Sandia National Laboratories. University of Southern California. California Institute of Technology and NASA Ames Research Center [5] Van Raemdonck GMR. Design of low drag bluff road vehicles. Doctoral design. Delft University of Technology. Faculty of Aerospace Engineering. May, 2012. [6] Goldstein RJ. Fluid mechanics measurements. Hemisphere Publishing Corporation; 1993. [7] Allen JM, Tudor DH. Charts for interpolation of local skin friction from experimental turbulent velocity profile. NASA SP-3048. 1969. [8] Preston JH. The determination of turbulent skin friction by means of Pitot tube. J Roy Aero Soc 1954;58. [9] Patel VC. Calibration of the Preston tube and limitation on its use in pressure gradient. J Fluid Mech 1965;23:185–208. [10] Bechert DW. Calibration of Preston tube. J AIAA 1995;34(1):205–6. [11] Schlichting H. Boundary layer theory. New York: McGraw-Hill; 1979. [12] Gracey W. Measurement of aircraft speed and altitude. NASA Reference Publication 1046; 1980. [13] Hoerner SF. Fluid-dynamic drag; practical information on aerodynamic drag and hydrodynamic resistance. Midland Park; 1965.